In this lesson, students add one-digit and two-digit numbers by composing a ten using place value reasoning and properties of operations. The associative and commutative property are highlighted in this lesson.

The first activity uses 10-frame diagrams to encourage students to determine how many ones can be added to a two-digit number to get to the next multiple of 10. Students consider decomposing a one-digit number in such a way that they can combine one part with the two-digit number to make a multiple of 10 ().

In the second activity, students compare different representations of this method, including those that use connecting cubes and base-ten drawings. These representations help students use their understanding of place value to see that when adding ones to ones, they can sometimes make a new unit of ten. This is a conceptual jump for students from understanding that they can count to a “10” (or the next ten) to understanding that they can create a new unit of ten from 10 ones (MP7).

How did the work of Activity 1 lay the foundation for students to be successful in the next activity? What do students need to be fluent with in order to use the method presented in Activity 2?